# Find the volume of a rectangular parallelepiped if the sum of its length and width is 56 cm, the sum of length

**Find the volume of a rectangular parallelepiped if the sum of its length and width is 56 cm, the sum of length and height is 65 cm, and the sum of the lengths of all edges is 360 cm.**

First of all, we find the values of three dimensions of a rectangular parallelepiped.

The sum of the lengths of all edges of a rectangular parallelepiped is equal to the product of 4 and the sum of all faces. Thus, the sum of all the faces of the rectangular parallelepiped is:

1) 360: 4 = 90 (cm).

Let’s calculate what the height is equal to if the sum of the length and width is 56 cm:

2) 90 – 56 = 34 (cm) – height.

Let us find what the length is equal to, if, according to the condition of the problem, the sum of the length and height is 65 cm:

3) 65 – 34 = 31 (cm) – length.

Now let’s calculate the width, knowing that the sum of the length and width is 56 cm:

4) 56 – 31 = 25 (cm) – width.

Let’s find the volume of a rectangular parallelepiped by the product of its three dimensions:

5) V = 25 * 31 * 34 = 26350 (cm³).

Answer: the volume of a rectangular parallelepiped is 26350 cm³.